A Concise Introduction to Pure Mathematics [Paperback]

Martin Liebeck (Author), M W Liebeck (Author)

Book Description

ISBN-10: 1584881933 | ISBN-13: 978-1584881933 | Publication Date: March 24, 2000 | Edition: 1

For many students interested in pursuing - or required to pursue - the study of mathematics, a critical gap exists between the level of their secondary school education and the background needed to understand, appreciate, and succeed in mathematics at the university level. A Concise Introduction to Pure Mathematics provides a robust bridge over this gap. In nineteen succinct chapters, it covers the range of topics needed to build a strong foundation for the study of the higher mathematics.

Sets and proofs Inequalities
Real numbers Decimals
Rational numbers Introduction to analysis
Complex numbers Polynomial equations
Induction Integers and prime numbers
Counting methods Countability
Functions Infinite sets
Platonic Solids Euler's Formula

Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It demystifies some of the perceived abstractions, intrigues its readers, and entices them to continue their exploration on to analysis, number theory, and beyond.

Editorial Reviews

Review

It would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. … A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering.
—Computing Reviews, November 2011

Now in an updated and expanded third edition, A Concise Introduction to Pure Mathematics provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics … . Of special note is the inclusion of solutions to all of the odd-numbered exercises. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college level mathematics curriculums, A Concise Introduction to Pure Mathematics is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index.
—Library Bookwatch, December 2010

This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.
—Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA

In addition to preparing students to go on in mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. … This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck’s writing style is clear and easy to read. This is a book that could be read by a student on his or her own. There is a wide selection of problems ranging from routine to quite challenging.
—From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA

Praise for Previous Editions:
The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … .
—Gerald A. Heuer, Zentralblatt MATH, 2009

…a pleasure to read … a very welcome and highly accessible book.
—Michael Ward, The Mathematical Gazette, March 2007

--This text refers to an alternate Paperback edition.

About the Author

Liebeck; M.W. Imperial College, London, England, UK,

Product Details

• Paperback: 176 pages
• Publisher: Chapman and Hall/CRC; 1 edition (March 24, 2000)
• Language: English
• ISBN-10: 1584881933
• ISBN-13: 978-1584881933
• Product Dimensions: 9.2 x 6.2 x 0.4 inches
• Shipping Weight: 10.1 ounces
• Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,928,059 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

27 of 27 people found the following review helpful:

4.0 out of 5 stars The missing link, October 2, 2000

By 

Joe Stauffer (Norman, OK United States) - See all my reviews
(REAL NAME)   

This review is from: A Concise Introduction to Pure Mathematics (Paperback)

I'm not sure how many of us there are out there, but I am one of a breed of consumers of applied mathematics who learned some pretty sophisticated mathematical technology without the rigor of pure mathematics. Although this book is aimed at freshmen entering mathematics programs who need to be inculturated into the world of pure mathematics, I found it to be the crucial link I needed to advance my own applied mathematical training. I reached a point where I was ready to move from applied texts to the more cryptic world of math texts written for graduate mathematicians. Unfortunately, I was not properly trained to decypher their special language and way of doing things, particularly that of the formal proof. I found reading introductory texts in analysis to be like trying to learn Japanese from books which were themselves written in Japanese. Then I found this wonderful little text. It made things much more accessible to me and helped me crack enough of the code where I could find my way around those analysis texts, which in turn allowed me to move on to the graduate math texts containing the methods I am studying now. The book is a bit high priced for its size, but for me it was well worth it.

7 of 7 people found the following review helpful:

4.0 out of 5 stars Nicely-written transition from high school to college mathematics. Targeted more toward classroom use than self-study, August 16, 2009

By 

Reader - See all my reviews

This review is from: A Concise Introduction to Pure Mathematics (Chapman Hall/Crc Mathematics) (Chapman Hall/CRC Mathematics Series) (Paperback)

This is a review of the (2005) 2nd ed. The number of texts covering the transition from secondary school to college mathematics has grown considerably in recent years. This is one of the better-written and well-organized texts. Its greatest concentration is on important concepts from pure mathematics, such as sets and numbers, real and complex, and some interesting topics from number theory. Explanations are clear and the in-text examples and proofs are well chosen and explained. The emphasis here is primarily on proofs rather than on the solution of applied problems. The author uses only the minimum level of mathematical rigor required, and this is supplemented by clear discussions. I enjoyed the gentle introduction to set theory and the in-text questions, followed by solutions. The proofs of propositions are clear and complete.

The Forward says this book can "be read by a student on his or her own". The Preface restates this slightly differently, by saying that as "well as being designed for use in a first university course, the book is also suitable for self-study". However, debatably, this text does not serve both purposes equally well, as it seems less suitable for a self-study target audience.

A " Solutions Manual for a Concise Introduction to Pure Mathematics" is listed on-line. The Solutions Manual described is about 70 pages in length. If this is correct, it's contents could easily have been included with this text, while still keeping the text relatively concise at less than 300 pages. At the time of this review, this manual was not available from Amazon or other on-line sellers.

The lack of fully-worked solutions to exercises is typical of many books designed for classroom use. This allows faculty to assign problems that students must work out on their own, as solutions are not readily available. While this approach is, arguably, appropriate for a classroom environment, the lack of detailed exercise solutions considerably reduces the value of this text for self-study. Mathematics is not a spectator sport, so the opportunity to work through a considerable variety of problems and check results against detailed solutions is quite important, particularly for self-study. The lack of fully-worked exercise solutions is perhaps the key deficiency of this text. However, it is enjoyable to read, with explanations that are very well done. Thus, although not self-contained, it could be excellent for self-study if supplemented appropriately with a problems book with fully-worked solutions.

6 of 6 people found the following review helpful:

5.0 out of 5 stars An excellent way to discover the basics of becoming a mathematician, October 2, 2008

By 

Rick - See all my reviews

This review is from: A Concise Introduction to Pure Mathematics (Chapman Hall/Crc Mathematics) (Chapman Hall/CRC Mathematics Series) (Paperback)

I encountered this book in my first proofs course, and it was a delight to read. My less dedicated classmates found the book too difficult, but I think it's just right for a student who has been curious about methods of proof and some of the more elementary parts of pure mathematics. Some of the problems are easy and some are pretty challenging, but I think they can all be solved especially if you've got access to people who know mathematics (and everyone on the internet has this is they look).